1. Field of the Invention
The invention relates to a control system to control a position parameter of a stage in a lithographic apparatus, to a lithographic apparatus including such control system and to a device manufacturing method.
2. Description of the Related Art
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
The lithographic apparatus includes a substrate table to hold the substrate. The substrate table is positioned under control of a control system to be able to position a target portion of the substrate substantially in a focal plane of a projection system of the lithographic apparatus. The control system thus operates in a coordinate system which is related to a position of the projection system or the position of an image formed by the projection system on the substrate. A substrate table position measurement system may be configured to provide a position measurement of the substrate table with respect to an origin of such coordinate system. Typically, this origin is located directly under a lens center, at a substrate level. A position of the substrate table is controlled with a plurality of controllers, each functioning in one of the coordinates as measured by the measurement system. For example, controllers may be present operating in X, Y, Z, Rx, Ry, Rz coordinates, the latter three describing rotations around the X, Y and Z axes, respectively. Hence, each of these controllers generates a controller force or torque (i.e. a controller output signal to drive an actuator which actuator will thereby generate a force or torque) as a response to the deviation of the actually measured position in its coordinate system from the corresponding position set-point. The forces and torques calculated this way by the controllers, are also defined in the coordinate system as defined above, related to the lens center.
However, a position of a center of mass of the substrate table may not coincide with the origin of this coordinate system. In particular, the position of the center of mass of the substrate table shifts as the position of the substrate table changes with respect to the mentioned coordinate system. Now, when for example the Rx controller generates a torque to accelerate the substrate table around the X axis, depending on the shift of the substrate table center of mass with respect to the coordinate system origin in Y direction, a Z acceleration will result, in turn resulting in a Z position error. This is caused by the fact that a torque in Rx direction on the stage tilts the stage around a line crossing the center of mass of the stage, and not around the origin of the coordinate system under the lens, as would be desired. The resulting error in Z direction results in a response of the Z controller to bring it down to zero, however at this point the Z error has already occurred, which is undesirable.
To correct for this effect, a transformation matrix called gain scheduling matrix is used. This matrix transforms the forces and torques as generated by the controllers in the above-described lens-related coordinate system to forces and torques in the substrate table coordinate system, defined by the position of its center of mass. In the above example, when the Rx controller generates a torque to accelerate the substrate table around the X axis, depending on the position of the substrate table in Y direction, an extra force in Z will be generated that corrects for the error in Z that would occur otherwise, as described above. The gain scheduling matrix then generates an extra force in Z that makes sure the substrate remains in the focal plane of the lens, and hence the table actually tilts around the X axis as defined by the coordinate system described above related to the lens, instead of tilting around a line extending in X direction, crossing the center of mass of the stage. The generated extra force in Z is proportional to the controller-generated torque around the X axis, the distance of the stage center of mass with respect to the coordinate system origin in Y direction and the stage mass, and inversely proportional to the inertia of the stage around the X axis.
Similar techniques are applied for torques around the Y and Z axes, impacting X, Y and Z position errors. The gain scheduling matrix makes sure that the controller forces and torques in the above-mentioned lens-related coordinate system are translated to forces and torques in the center-of-mass related coordinate system of the substrate table. These forces and torques are then applied to the substrate table using actuators, that are naturally connected to a location which is fixed with respect to the substrate table's center of mass.
However, disturbance forces and disturbance torques act directly on the stage, as they naturally do not follow the gain scheduling compensation used for controller-generated forces and torques. As a result thereof, disturbance torques do have an influence on other directions. As an example, if the stage is positioned off-center, a disturbance torque which would tend to tilt the stage with respect to an axis extending along the plane of focus of the projection system and through the center of mass of the stage, would result in a vertical position error of the target portion under the lens center because of the tilting of the stage. In this context the term vertical should be understood as being a direction perpendicular to the plane of focus. As a result thereof, disturbance torques may result in focus errors hence resulting in a deterioration of an accuracy of the pattern to be projected on to the substrate. It is noted that if the torque would not be acting on the stage as a disturbance torque, but would have been generated by the controller as a signal to effectuate such a torque, the gain scheduling matrix would have added a force in the vertical direction to compensate for the above-mentioned effect of a displacement in vertical direction. Thus the gain scheduling matrix can effectively suppress the above effect when caused by a torque by the controller, however may not suppress this effect in case of a disturbance torque.